Question

\(\left(\dfrac{x+1}{x-1}\right)^2-6\left(\dfrac{x+1}{x-1}\right)+5=0\) 

giải phương trình

Answer 1

ĐKXĐ: \(x\ne1\)

Đặt \(\dfrac{x+1}{x-1}=t\)

\(\Rightarrow t^2-6t+5=0\Leftrightarrow\left(t-1\right)\left(t-5\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}t=1\\t=5\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}\dfrac{x+1}{x-1}=1\\\dfrac{x+1}{x-1}=5\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x+1=x-1\left(vô-nghiệm\right)\\x+1=5x-5\end{matrix}\right.\)

\(\Rightarrow x=\dfrac{3}{2}\)